1. Field of the Invention
The present invention relates to a MOSFET (metal oxide semiconductor field effect transistor) in a semiconductor device and, in particular, to a hyperbolic type channel MOSFET capable of increasing a drain current by determining the width of a channel region according to distances from a source region and a drain region.
2. Description of the Related Art
In recent years, the packaging density of the semiconductor device is increasing and hence a further fine patterning has been required also in the MOSFET. For this reason, the drain current density in the MOSFET has been required to increase.
In order to increase a drain current, there has been conventionally used a method of utilizing the overshoot effect of a carrier. The overshoot effect of a carrier is produced by applying a strong electric field to a channel region of a MOSFET and by shortening the length of the channel region from a source region to a drain region (hereinafter referred to as xe2x80x9cchannel region lengthxe2x80x9d).
In a conventional MOSFET, however, there is presented a problem that even if the electric field applied to the channel region is made stronger, a current is not so much increased. FIG. 1 is a plan view to show the configuration of a conventional MOSFET. As shown in FIG. 1, the conventional MOSFET is composed of a source region 11, a drain region 12, and a channel region 13 disposed between the source region 11 and the drain region 12. The channel region 13 is rectangular. That is, the width of the channel region 13 is set at a constant value W0 along the entire length from the end of the source region 11 side to the end of the drain region 12 side. Further, the width of the source 11 region and the width of the drain region 12 are equal to the width of the neighboring channel region 13. Still further, an insulating layer 14 is formed on the channel region 13 (at the front side of the paper in FIG. 1) and a gate 15 is formed on the insulating layer 14.
In the channel region 13 of the MOSFET shown in FIG. 1, as a position comes near to the end of the drain region 12 side from the end of the source region 11 side along the channel, a difference between a channel potential and a gate potential decreases and the amount of carriers induced in an inversion layer decreases. Since a current continuity law is established in the direction of channel, in order to realize the drain current of a predetermined magnitude to compensate the decreased amount of carriers, a stronger electric field is required to be applied to the channel region to drift the carriers. However, as described above, the amount of carriers in the channel region 13 decreases as the position comes near to the drain region 12 and hence the channel potential increases in gradient as the position comes near to the drain region 12, and hence the potential difference between the source region 11 and the drain region 12 is applied mainly to the vicinity of the drain side end of the channel region 13.
FIG. 2 is a graph to show a channel potential distribution in the conventional MOSFET, in which a horizontal axis designates a distance x from the end of the source region 11 side of the channel region 13 to the direction toward the drain region 12 side and a vertical axis designates a channel potential Vcs0. As shown in FIG. 2, since a very strong electric field is not applied in the direction of the channel in the source region 11 side of the channel region 13, even if the MOSFET has a short channel length, it can not sufficiently benefit the velocity overshoot effect of the carriers because it is hard to produce the velocity overshoot effect of the carriers. As a result, the conventional MOSFET presents a problem that even if the channel length is made short, a drain current value is not improved so much.
An object of the present invention is to provide a MOSFET capable of making the strength of the electric field uniform in the direction of a channel and increasing a drain current.
A MOSFET according to the present invention comprises: a source region; a drain region; and a channel region disposed between the source region and the drain region. In the channel region, the width of the channel region changes according to the following mathematical equation (1).                               W          ⁡                      (            x            )                          =                                                                                                                        4                      ⁢                                                                        {                                                                                                                    (                                                                  1                                  +                                  δ                                                                )                                                            ⁢                                                              E                                sat                                                            ⁢                              L                                                        +                                                          V                              DD                                                        -                                                          V                              T                                                                                }                                                2                                                              +                                                                                                                                          {                                                                                                    (                                                          1                              +                              δ                                                        )                                                    ⁢                                                      E                            sat                                                    ⁢                          L                                                +                                                  2                          ⁢                                                      (                                                                                          V                                DD                                                            -                                                              V                                T                                                                                      )                                                                                              }                                        ⁢                                          (                                                                        V                          DD                                                -                                                  V                          T                                                                    )                                                                                                          6              ⁢                              {                                                                            (                                              1                        +                        δ                                            )                                        ⁢                                          E                      sat                                        ⁢                                          L                      ⁡                                              (                                                  1                          -                                                      x                            L                                                                          )                                                                              +                                      V                    DD                                    -                                      V                    T                                                  }                            ⁢                              {                                                                            (                                              1                        +                        δ                                            )                                        ⁢                                          E                      sat                                        ⁢                    L                                    +                                      V                    DD                                    -                                      V                    T                                                  }                                              ⁢                      W            O                                              (        1        )            
In equation (1), x denotes a distance from the end of the source region side to the direction toward the drain region side, W(x) denotes the width of the channel region at the position of the distance x, xcex4 denotes a substrate charge effect coefficient, L denotes the length from the end of the source region side to the end of the drain side, VDD denotes a gate voltage, VT denotes a threshold voltage, WO denotes a standard width of the channel region, and Esat denotes a strength of a carrier velocity saturation electric field.
In the present invention, by setting the width of the channel region at the value described above, the total amount of carriers in the direction of width at a position in the channel is not dependent on a distance from the source region and the drain region but is made constant, so an electric field of the same strength can be applied to the entire channel region to maximize a drain current.
Further, it is preferably that, in the above-mentioned MOSFET, the width of the source region is equal to or larger than the width of the channel region at the source region side and the width of the drain region is equal to or larger than the width of the channel region at the end of the drain region side. This can produce the effect described above to a maximum level.